Influence of archwire and bracket dimensions on sliding mechanics: derivations and determinations of the critical contact angles for binding.

There is every indication that classical friction controls sliding mechanics below some critical contact angle, theta c. Once that angle is exceeded, however, binding and notching phenomena increasingly restrict sliding mechanics. Using geometric archwire and bracket parameters, the theta c is calculated as the boundary between classical frictional behaviour and binding-related phenomena. What these equations predict is independent of practitioner or technique. From these derivations two dimensionless numbers are also identified as the bracket and the engagement index. The first shows how the width of a bracket compares to its Slot; the second indicates how completely the wire fills the Slot. When nominal wire and bracket dimensions are calculated for both standard Slots, the maximum theta c theoretically equals 3.7 degrees. Thus, knowledge of the archwire or bracket alone is insufficient; knowledge of the archwire-bracket combination is necessary for theta c to be calculated. Once calculated, sliding mechanics should be initiated only after the contact angle, theta, approaches the characteristic value of theta c for the particular archwire-bracket combination of choice--that is, when theta approximately theta c.